Question

Let \( A = \{1, 3, 7, 9, 11\} \) and \( B = \{2, 4, 5, 7, 8, 10, 12\} \). Then the total number of one-one maps \( f: A \to B \), such that \( f(1) + f(3) = 14 \), is:

• A. 180
• B. 120
• C. 480
• D. 240

Answer 1

The Correct Option is D

 

Given sets:

\[ A = \{1, 3, 7, 9, 11\} \quad \text{and} \quad B = \{2, 4, 5, 7, 8, 10, 12\} \]

\[ A = \{1, 3, 7, 9, 11\} \]

\[ B = \{2, 4, 5, 7, 8, 10, 12\} \]

\[ f(1) + f(3) = 14 \]

(i) \( 2 + 12 \)

(ii) \( 4 + 10 \)

\[ 2 \times (2 \times 5 \times 4 \times 3) = 240 \]